14. Production Scheduling. A simple model is sometimes used in order to illustrate the production-scheduling maxim, "bal- ance flow, not capacity." Consider a factory that consists of three workstations where each customer order must proceed through the workstations in sequence. Next, suppose that the workloads are balanced, which means that, on average, each order requires equal amounts of work at each of the three stations. Assume that the average operation time is 60 minutes. Now suppose that six orders are to be scheduled tomor- row. Using average times, we would expect that completion times would look like the following: Order 1 2 3 4 5 6 Complete Station 1 60 Complete Station 2 120 120 180 180 240 300 360 240 300 360 420 Complete Station 3 180 240 300 360 420 480 and we would expect that the schedule length would be 480 minutes. Suppose that actual operation times are random and follow a triangular distribution with a minimum of 30 minutes and a maximum of 90 minutes. Note: no order can start at a station until the previous order has finished. a. What is the mean schedule length? b. What is the probability that the schedule length will exceed 480 minutes? c. Change the range of the distribution from 60 to 40 and to 20, and then repeat (a) and (b). What is the mean schedule length in each case? What do you conclude from these observations?